DOI Page / Citation link:
https://doi.org/10.11588/diglit.6444#0025
16 KAHUN PAPYKI.
to 2 -f- 99, with proofs and a few explanatory
words, and further gains in clearness by the
use of red ink as well as black.
The strip pasted on to the back of our
papyrus has slipped slightly since the table
was written; hence some of the characters,
especially the fraction f in 1. 5, have lost their
form.
Kahun, IV. 3.
[PI. VIII., cols. 11-14.]
Found at Kahun with the last. Length,
16f in. = 42-5 cm. Width, 5 in. = 12-5 cm.
At 2 in. = 5 cm. from the right edge there is
a join : the rest is without join. The papyrus
is quite perfect.
Recto.—Arithmetical calculations and traces
of palimpsest.
Verso.—Blank.
It may be worth while to remind the reader
that adding and subtracting, doubling and
halving, multiplying by 10 and dividing by 10
—and strange to say multiplying by ^ ( = f-)—
formed the basis of all Egyptian arithmetic.
could only be reached through halving f.
Also, that when in a column of figures certain
figures are required again, while others could
be neglected, the former were often marked by
a dash at the side, as here in cols. 11, 13, 14.
The arithmetical operations in this papyrus
are as follows : —
Col. 14, 11. 3-5. l| of 12 is found to be 16 ;
11. 6-9, the number 16 is squared, giving 256.
Col. 13. 256 is multiplied by 5-g-, giving
1365-g-, which number we see written inside a
broad, somewhat oval figure in Col. 14, with
12 and 8 written outside the circumference.
It would seem as though the problem had
been to find the contents of a circular granary,
of which the height and the diameter were 12
and 8 cubits respectively; but if so, the method
adopted and the result are quite wrong, whether
we look for the answer in cubits cubed, in Ichar
( = § cubits cubed), or in quadruple heqat}
Col. 12, 11. 1, 2. The number 110 having
apparently been divided by 8 gives ljj-f-j^.
In the following lines xf is subtracted 9 times
from 13f and its successive remainders.
Col. 11. 1-^- is multiplied 9 times, giving
3|t2- (H 10 be added to this, making 13f^
we obtain the value of 110 -r 8, as in Col. 12,
11. 1, 2; and if 10 be subtracted from the figures
in Col. 12, 1. 6, we obtain |xj.)
I must confess that I do not see the con-
nexion between these operations; but probably
they are all parts of one problem.
Kahun, XLV. 1.
[PL VIII., 11. 15-22.]
These fragments {verso blank) are useful
as showing the hieratic forms of the highest
numerals. I do not see what the very large
quantities mentioned are likely to refer to :
they diminish rapidly in succeeding lines, but
apparently not in any fixed proportion. Yet
it seems probable that they formed part of a
considerable mathematical calculation, and not
of mere accounts.
Kahun, LV. 3.
[PI. VIII., 11. 23-29.]
Found at Kahun, November, 1889. Original
length unknown. Width, 5f inches = 14'5 cm.
1 A friend (Mr. Chas. Heape, of Kochdale), pointing out
that the calculation in Cols. 13 and 14 gives actually the
contents of a space 16 x 16 X y, all worked from 12,
suggests that the problem may have been to find the con-
tents of a square building, the height of which was J the
length and width, and the length of the side J more than
12 (cubits). The oval figure in Col. 14 may indicate an
enclosed space of any form in a general way, and this is
certainly the best solution yet proposed.
to 2 -f- 99, with proofs and a few explanatory
words, and further gains in clearness by the
use of red ink as well as black.
The strip pasted on to the back of our
papyrus has slipped slightly since the table
was written; hence some of the characters,
especially the fraction f in 1. 5, have lost their
form.
Kahun, IV. 3.
[PI. VIII., cols. 11-14.]
Found at Kahun with the last. Length,
16f in. = 42-5 cm. Width, 5 in. = 12-5 cm.
At 2 in. = 5 cm. from the right edge there is
a join : the rest is without join. The papyrus
is quite perfect.
Recto.—Arithmetical calculations and traces
of palimpsest.
Verso.—Blank.
It may be worth while to remind the reader
that adding and subtracting, doubling and
halving, multiplying by 10 and dividing by 10
—and strange to say multiplying by ^ ( = f-)—
formed the basis of all Egyptian arithmetic.
could only be reached through halving f.
Also, that when in a column of figures certain
figures are required again, while others could
be neglected, the former were often marked by
a dash at the side, as here in cols. 11, 13, 14.
The arithmetical operations in this papyrus
are as follows : —
Col. 14, 11. 3-5. l| of 12 is found to be 16 ;
11. 6-9, the number 16 is squared, giving 256.
Col. 13. 256 is multiplied by 5-g-, giving
1365-g-, which number we see written inside a
broad, somewhat oval figure in Col. 14, with
12 and 8 written outside the circumference.
It would seem as though the problem had
been to find the contents of a circular granary,
of which the height and the diameter were 12
and 8 cubits respectively; but if so, the method
adopted and the result are quite wrong, whether
we look for the answer in cubits cubed, in Ichar
( = § cubits cubed), or in quadruple heqat}
Col. 12, 11. 1, 2. The number 110 having
apparently been divided by 8 gives ljj-f-j^.
In the following lines xf is subtracted 9 times
from 13f and its successive remainders.
Col. 11. 1-^- is multiplied 9 times, giving
3|t2- (H 10 be added to this, making 13f^
we obtain the value of 110 -r 8, as in Col. 12,
11. 1, 2; and if 10 be subtracted from the figures
in Col. 12, 1. 6, we obtain |xj.)
I must confess that I do not see the con-
nexion between these operations; but probably
they are all parts of one problem.
Kahun, XLV. 1.
[PL VIII., 11. 15-22.]
These fragments {verso blank) are useful
as showing the hieratic forms of the highest
numerals. I do not see what the very large
quantities mentioned are likely to refer to :
they diminish rapidly in succeeding lines, but
apparently not in any fixed proportion. Yet
it seems probable that they formed part of a
considerable mathematical calculation, and not
of mere accounts.
Kahun, LV. 3.
[PI. VIII., 11. 23-29.]
Found at Kahun, November, 1889. Original
length unknown. Width, 5f inches = 14'5 cm.
1 A friend (Mr. Chas. Heape, of Kochdale), pointing out
that the calculation in Cols. 13 and 14 gives actually the
contents of a space 16 x 16 X y, all worked from 12,
suggests that the problem may have been to find the con-
tents of a square building, the height of which was J the
length and width, and the length of the side J more than
12 (cubits). The oval figure in Col. 14 may indicate an
enclosed space of any form in a general way, and this is
certainly the best solution yet proposed.